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isl_mat_swap_cols: add memory management annotations
[isl.git] / isl_mat.c
blob6f957e55dc982c8bf9d4b8b7104d532709eb99a6
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2014 Ecole Normale Superieure
4 *
5 * Use of this software is governed by the MIT license
6 *
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
10 */
11
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl/space.h>
15 #include <isl_seq.h>
16 #include <isl_mat_private.h>
17 #include <isl_vec_private.h>
18 #include <isl_space_private.h>
19 #include <isl_val_private.h>
20 #include <isl/deprecated/mat_int.h>
21
22 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
23 {
24 return mat ? mat->ctx : NULL;
25 }
26
27 /* Return a hash value that digests "mat".
28 */
29 uint32_t isl_mat_get_hash(__isl_keep isl_mat *mat)
30 {
31 int i;
32 uint32_t hash;
33
34 if (!mat)
35 return 0;
36
37 hash = isl_hash_init();
38 isl_hash_byte(hash, mat->n_row & 0xFF);
39 isl_hash_byte(hash, mat->n_col & 0xFF);
40 for (i = 0; i < mat->n_row; ++i) {
41 uint32_t row_hash;
42
43 row_hash = isl_seq_get_hash(mat->row[i], mat->n_col);
44 isl_hash_hash(hash, row_hash);
45 }
46
47 return hash;
48 }
49
50 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
51 unsigned n_row, unsigned n_col)
52 {
53 int i;
54 struct isl_mat *mat;
55
56 mat = isl_alloc_type(ctx, struct isl_mat);
57 if (!mat)
58 return NULL;
59
60 mat->row = NULL;
61 mat->block = isl_blk_alloc(ctx, n_row * n_col);
62 if (isl_blk_is_error(mat->block))
63 goto error;
64 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
65 if (n_row && !mat->row)
66 goto error;
67
68 for (i = 0; i < n_row; ++i)
69 mat->row[i] = mat->block.data + i * n_col;
70
71 mat->ctx = ctx;
72 isl_ctx_ref(ctx);
73 mat->ref = 1;
74 mat->n_row = n_row;
75 mat->n_col = n_col;
76 mat->max_col = n_col;
77 mat->flags = 0;
78
79 return mat;
80 error:
81 isl_blk_free(ctx, mat->block);
82 free(mat);
83 return NULL;
84 }
85
86 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
87 unsigned n_row, unsigned n_col)
88 {
89 int i;
90 isl_int *old;
91 isl_int **row;
92
93 if (!mat)
94 return NULL;
95
96 if (mat->max_col >= n_col && mat->n_row >= n_row) {
97 if (mat->n_col < n_col)
98 mat->n_col = n_col;
99 return mat;
100 }
101
102 if (mat->max_col < n_col) {
103 struct isl_mat *new_mat;
104
105 if (n_row < mat->n_row)
106 n_row = mat->n_row;
107 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
108 if (!new_mat)
109 goto error;
110 for (i = 0; i < mat->n_row; ++i)
111 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
112 isl_mat_free(mat);
113 return new_mat;
114 }
115
116 mat = isl_mat_cow(mat);
117 if (!mat)
118 goto error;
119
120 old = mat->block.data;
121 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
122 if (isl_blk_is_error(mat->block))
123 goto error;
124 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
125 if (n_row && !row)
126 goto error;
127 mat->row = row;
128
129 for (i = 0; i < mat->n_row; ++i)
130 mat->row[i] = mat->block.data + (mat->row[i] - old);
131 for (i = mat->n_row; i < n_row; ++i)
132 mat->row[i] = mat->block.data + i * mat->max_col;
133 mat->n_row = n_row;
134 if (mat->n_col < n_col)
135 mat->n_col = n_col;
136
137 return mat;
138 error:
139 isl_mat_free(mat);
140 return NULL;
141 }
142
143 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
144 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
145 {
146 int i;
147 struct isl_mat *mat;
148
149 mat = isl_alloc_type(ctx, struct isl_mat);
150 if (!mat)
151 return NULL;
152 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
153 if (n_row && !mat->row)
154 goto error;
155 for (i = 0; i < n_row; ++i)
156 mat->row[i] = row[first_row+i] + first_col;
157 mat->ctx = ctx;
158 isl_ctx_ref(ctx);
159 mat->ref = 1;
160 mat->n_row = n_row;
161 mat->n_col = n_col;
162 mat->block = isl_blk_empty();
163 mat->flags = ISL_MAT_BORROWED;
164 return mat;
165 error:
166 free(mat);
167 return NULL;
168 }
169
170 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
171 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
172 {
173 if (!mat)
174 return NULL;
175 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
176 first_col, n_col);
177 }
178
179 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
180 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
181 {
182 int i;
183
184 for (i = 0; i < n_row; ++i)
185 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
186 }
187
188 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
189 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
190 {
191 int i;
192
193 for (i = 0; i < n_row; ++i)
194 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
195 }
196
197 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
198 {
199 if (!mat)
200 return NULL;
201
202 mat->ref++;
203 return mat;
204 }
205
206 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
207 {
208 int i;
209 struct isl_mat *mat2;
210
211 if (!mat)
212 return NULL;
213 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
214 if (!mat2)
215 return NULL;
216 for (i = 0; i < mat->n_row; ++i)
217 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
218 return mat2;
219 }
220
221 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
222 {
223 struct isl_mat *mat2;
224 if (!mat)
225 return NULL;
226
227 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
228 return mat;
229
230 mat2 = isl_mat_dup(mat);
231 isl_mat_free(mat);
232 return mat2;
233 }
234
235 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat)
236 {
237 if (!mat)
238 return NULL;
239
240 if (--mat->ref > 0)
241 return NULL;
242
243 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
244 isl_blk_free(mat->ctx, mat->block);
245 isl_ctx_deref(mat->ctx);
246 free(mat->row);
247 free(mat);
248
249 return NULL;
250 }
251
252 int isl_mat_rows(__isl_keep isl_mat *mat)
253 {
254 return mat ? mat->n_row : -1;
255 }
256
257 int isl_mat_cols(__isl_keep isl_mat *mat)
258 {
259 return mat ? mat->n_col : -1;
260 }
261
262 /* Check that "col" is a valid column position for "mat".
263 */
264 static isl_stat check_col(__isl_keep isl_mat *mat, int col)
265 {
266 if (!mat)
267 return isl_stat_error;
268 if (col < 0 || col >= mat->n_col)
269 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
270 "column out of range", return isl_stat_error);
271 return isl_stat_ok;
272 }
273
274 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
275 {
276 if (!mat)
277 return -1;
278 if (row < 0 || row >= mat->n_row)
279 isl_die(mat->ctx, isl_error_invalid, "row out of range",
280 return -1);
281 if (check_col(mat, col) < 0)
282 return -1;
283 isl_int_set(*v, mat->row[row][col]);
284 return 0;
285 }
286
287 /* Extract the element at row "row", oolumn "col" of "mat".
288 */
289 __isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,
290 int row, int col)
291 {
292 isl_ctx *ctx;
293
294 if (!mat)
295 return NULL;
296 ctx = isl_mat_get_ctx(mat);
297 if (row < 0 || row >= mat->n_row)
298 isl_die(ctx, isl_error_invalid, "row out of range",
299 return NULL);
300 if (check_col(mat, col) < 0)
301 return NULL;
302 return isl_val_int_from_isl_int(ctx, mat->row[row][col]);
303 }
304
305 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
306 int row, int col, isl_int v)
307 {
308 mat = isl_mat_cow(mat);
309 if (!mat)
310 return NULL;
311 if (row < 0 || row >= mat->n_row)
312 isl_die(mat->ctx, isl_error_invalid, "row out of range",
313 goto error);
314 if (check_col(mat, col) < 0)
315 return isl_mat_free(mat);
316 isl_int_set(mat->row[row][col], v);
317 return mat;
318 error:
319 isl_mat_free(mat);
320 return NULL;
321 }
322
323 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
324 int row, int col, int v)
325 {
326 mat = isl_mat_cow(mat);
327 if (!mat)
328 return NULL;
329 if (row < 0 || row >= mat->n_row)
330 isl_die(mat->ctx, isl_error_invalid, "row out of range",
331 goto error);
332 if (check_col(mat, col) < 0)
333 return isl_mat_free(mat);
334 isl_int_set_si(mat->row[row][col], v);
335 return mat;
336 error:
337 isl_mat_free(mat);
338 return NULL;
339 }
340
341 /* Replace the element at row "row", column "col" of "mat" by "v".
342 */
343 __isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,
344 int row, int col, __isl_take isl_val *v)
345 {
346 if (!v)
347 return isl_mat_free(mat);
348 if (!isl_val_is_int(v))
349 isl_die(isl_val_get_ctx(v), isl_error_invalid,
350 "expecting integer value", goto error);
351 mat = isl_mat_set_element(mat, row, col, v->n);
352 isl_val_free(v);
353 return mat;
354 error:
355 isl_val_free(v);
356 return isl_mat_free(mat);
357 }
358
359 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
360 {
361 int i;
362 struct isl_mat *mat;
363
364 mat = isl_mat_alloc(ctx, n_row, n_row);
365 if (!mat)
366 return NULL;
367 for (i = 0; i < n_row; ++i) {
368 isl_seq_clr(mat->row[i], i);
369 isl_int_set(mat->row[i][i], d);
370 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
371 }
372
373 return mat;
374 }
375
376 /* Create an "n_row" by "n_col" matrix with zero elements.
377 */
378 __isl_give isl_mat *isl_mat_zero(isl_ctx *ctx, unsigned n_row, unsigned n_col)
379 {
380 int i;
381 isl_mat *mat;
382
383 mat = isl_mat_alloc(ctx, n_row, n_col);
384 if (!mat)
385 return NULL;
386 for (i = 0; i < n_row; ++i)
387 isl_seq_clr(mat->row[i], n_col);
388
389 return mat;
390 }
391
392 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
393 {
394 if (!ctx)
395 return NULL;
396 return isl_mat_diag(ctx, n_row, ctx->one);
397 }
398
399 /* Is "mat" a (possibly scaled) identity matrix?
400 */
401 int isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)
402 {
403 int i;
404
405 if (!mat)
406 return -1;
407 if (mat->n_row != mat->n_col)
408 return 0;
409
410 for (i = 0; i < mat->n_row; ++i) {
411 if (isl_seq_first_non_zero(mat->row[i], i) != -1)
412 return 0;
413 if (isl_int_ne(mat->row[0][0], mat->row[i][i]))
414 return 0;
415 if (isl_seq_first_non_zero(mat->row[i] + i + 1,
416 mat->n_col - (i + 1)) != -1)
417 return 0;
418 }
419
420 return 1;
421 }
422
423 __isl_give isl_vec *isl_mat_vec_product(__isl_take isl_mat *mat,
424 __isl_take isl_vec *vec)
425 {
426 int i;
427 struct isl_vec *prod;
428
429 if (!mat || !vec)
430 goto error;
431
432 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
433
434 prod = isl_vec_alloc(mat->ctx, mat->n_row);
435 if (!prod)
436 goto error;
437
438 for (i = 0; i < prod->size; ++i)
439 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
440 &prod->block.data[i]);
441 isl_mat_free(mat);
442 isl_vec_free(vec);
443 return prod;
444 error:
445 isl_mat_free(mat);
446 isl_vec_free(vec);
447 return NULL;
448 }
449
450 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
451 __isl_take isl_vec *vec)
452 {
453 struct isl_mat *vec_mat;
454 int i;
455
456 if (!mat || !vec)
457 goto error;
458 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
459 if (!vec_mat)
460 goto error;
461 for (i = 0; i < vec->size; ++i)
462 isl_int_set(vec_mat->row[i][0], vec->el[i]);
463 vec_mat = isl_mat_inverse_product(mat, vec_mat);
464 isl_vec_free(vec);
465 if (!vec_mat)
466 return NULL;
467 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
468 if (vec)
469 for (i = 0; i < vec->size; ++i)
470 isl_int_set(vec->el[i], vec_mat->row[i][0]);
471 isl_mat_free(vec_mat);
472 return vec;
473 error:
474 isl_mat_free(mat);
475 isl_vec_free(vec);
476 return NULL;
477 }
478
479 __isl_give isl_vec *isl_vec_mat_product(__isl_take isl_vec *vec,
480 __isl_take isl_mat *mat)
481 {
482 int i, j;
483 struct isl_vec *prod;
484
485 if (!mat || !vec)
486 goto error;
487
488 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
489
490 prod = isl_vec_alloc(mat->ctx, mat->n_col);
491 if (!prod)
492 goto error;
493
494 for (i = 0; i < prod->size; ++i) {
495 isl_int_set_si(prod->el[i], 0);
496 for (j = 0; j < vec->size; ++j)
497 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
498 }
499 isl_mat_free(mat);
500 isl_vec_free(vec);
501 return prod;
502 error:
503 isl_mat_free(mat);
504 isl_vec_free(vec);
505 return NULL;
506 }
507
508 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
509 struct isl_mat *right)
510 {
511 int i;
512 struct isl_mat *sum;
513
514 if (!left || !right)
515 goto error;
516
517 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
518 isl_assert(left->ctx, left->n_row >= 1, goto error);
519 isl_assert(left->ctx, left->n_col >= 1, goto error);
520 isl_assert(left->ctx, right->n_col >= 1, goto error);
521 isl_assert(left->ctx,
522 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
523 goto error);
524 isl_assert(left->ctx,
525 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
526 goto error);
527
528 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
529 if (!sum)
530 goto error;
531 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
532 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
533 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
534
535 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
536 for (i = 1; i < sum->n_row; ++i) {
537 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
538 isl_int_addmul(sum->row[i][0],
539 right->row[0][0], right->row[i][0]);
540 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
541 left->n_col-1);
542 isl_seq_scale(sum->row[i]+left->n_col,
543 right->row[i]+1, right->row[0][0],
544 right->n_col-1);
545 }
546
547 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
548 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
549 isl_mat_free(left);
550 isl_mat_free(right);
551 return sum;
552 error:
553 isl_mat_free(left);
554 isl_mat_free(right);
555 return NULL;
556 }
557
558 static void exchange(struct isl_mat *M, struct isl_mat **U,
559 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
560 {
561 int r;
562 for (r = row; r < M->n_row; ++r)
563 isl_int_swap(M->row[r][i], M->row[r][j]);
564 if (U) {
565 for (r = 0; r < (*U)->n_row; ++r)
566 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
567 }
568 if (Q)
569 isl_mat_swap_rows(*Q, i, j);
570 }
571
572 static void subtract(struct isl_mat *M, struct isl_mat **U,
573 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
574 {
575 int r;
576 for (r = row; r < M->n_row; ++r)
577 isl_int_submul(M->row[r][j], m, M->row[r][i]);
578 if (U) {
579 for (r = 0; r < (*U)->n_row; ++r)
580 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
581 }
582 if (Q) {
583 for (r = 0; r < (*Q)->n_col; ++r)
584 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
585 }
586 }
587
588 static void oppose(struct isl_mat *M, struct isl_mat **U,
589 struct isl_mat **Q, unsigned row, unsigned col)
590 {
591 int r;
592 for (r = row; r < M->n_row; ++r)
593 isl_int_neg(M->row[r][col], M->row[r][col]);
594 if (U) {
595 for (r = 0; r < (*U)->n_row; ++r)
596 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
597 }
598 if (Q)
599 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
600 }
601
602 /* Given matrix M, compute
603 *
604 * M U = H
605 * M = H Q
606 *
607 * with U and Q unimodular matrices and H a matrix in column echelon form
608 * such that on each echelon row the entries in the non-echelon column
609 * are non-negative (if neg == 0) or non-positive (if neg == 1)
610 * and strictly smaller (in absolute value) than the entries in the echelon
611 * column.
612 * If U or Q are NULL, then these matrices are not computed.
613 */
614 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
615 struct isl_mat **U, struct isl_mat **Q)
616 {
617 isl_int c;
618 int row, col;
619
620 if (U)
621 *U = NULL;
622 if (Q)
623 *Q = NULL;
624 if (!M)
625 goto error;
626 M = isl_mat_cow(M);
627 if (!M)
628 goto error;
629 if (U) {
630 *U = isl_mat_identity(M->ctx, M->n_col);
631 if (!*U)
632 goto error;
633 }
634 if (Q) {
635 *Q = isl_mat_identity(M->ctx, M->n_col);
636 if (!*Q)
637 goto error;
638 }
639
640 col = 0;
641 isl_int_init(c);
642 for (row = 0; row < M->n_row; ++row) {
643 int first, i, off;
644 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
645 if (first == -1)
646 continue;
647 first += col;
648 if (first != col)
649 exchange(M, U, Q, row, first, col);
650 if (isl_int_is_neg(M->row[row][col]))
651 oppose(M, U, Q, row, col);
652 first = col+1;
653 while ((off = isl_seq_first_non_zero(M->row[row]+first,
654 M->n_col-first)) != -1) {
655 first += off;
656 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
657 subtract(M, U, Q, row, col, first, c);
658 if (!isl_int_is_zero(M->row[row][first]))
659 exchange(M, U, Q, row, first, col);
660 else
661 ++first;
662 }
663 for (i = 0; i < col; ++i) {
664 if (isl_int_is_zero(M->row[row][i]))
665 continue;
666 if (neg)
667 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
668 else
669 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
670 if (isl_int_is_zero(c))
671 continue;
672 subtract(M, U, Q, row, col, i, c);
673 }
674 ++col;
675 }
676 isl_int_clear(c);
677
678 return M;
679 error:
680 if (Q) {
681 isl_mat_free(*Q);
682 *Q = NULL;
683 }
684 if (U) {
685 isl_mat_free(*U);
686 *U = NULL;
687 }
688 isl_mat_free(M);
689 return NULL;
690 }
691
692 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
693 {
694 int i, rank;
695 struct isl_mat *U = NULL;
696 struct isl_mat *K;
697
698 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
699 if (!mat || !U)
700 goto error;
701
702 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
703 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
704 ++i;
705 if (i >= mat->n_row)
706 break;
707 }
708 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
709 if (!K)
710 goto error;
711 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
712 isl_mat_free(mat);
713 isl_mat_free(U);
714 return K;
715 error:
716 isl_mat_free(mat);
717 isl_mat_free(U);
718 return NULL;
719 }
720
721 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
722 {
723 int i;
724 struct isl_mat *mat2;
725
726 if (!mat)
727 return NULL;
728 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
729 if (!mat2)
730 goto error;
731 isl_int_set_si(mat2->row[0][0], 1);
732 isl_seq_clr(mat2->row[0]+1, mat->n_col);
733 for (i = 0; i < mat->n_row; ++i) {
734 isl_int_set_si(mat2->row[1+i][0], 0);
735 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
736 }
737 isl_mat_free(mat);
738 return mat2;
739 error:
740 isl_mat_free(mat);
741 return NULL;
742 }
743
744 /* Given two matrices M1 and M2, return the block matrix
745 *
746 * [ M1 0 ]
747 * [ 0 M2 ]
748 */
749 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
750 __isl_take isl_mat *mat2)
751 {
752 int i;
753 isl_mat *mat;
754
755 if (!mat1 || !mat2)
756 goto error;
757
758 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
759 mat1->n_col + mat2->n_col);
760 if (!mat)
761 goto error;
762 for (i = 0; i < mat1->n_row; ++i) {
763 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
764 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
765 }
766 for (i = 0; i < mat2->n_row; ++i) {
767 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
768 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
769 mat2->row[i], mat2->n_col);
770 }
771 isl_mat_free(mat1);
772 isl_mat_free(mat2);
773 return mat;
774 error:
775 isl_mat_free(mat1);
776 isl_mat_free(mat2);
777 return NULL;
778 }
779
780 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
781 {
782 int i;
783
784 for (i = 0; i < n_row; ++i)
785 if (!isl_int_is_zero(row[i][col]))
786 return i;
787 return -1;
788 }
789
790 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
791 {
792 int i, min = row_first_non_zero(row, n_row, col);
793 if (min < 0)
794 return -1;
795 for (i = min + 1; i < n_row; ++i) {
796 if (isl_int_is_zero(row[i][col]))
797 continue;
798 if (isl_int_abs_lt(row[i][col], row[min][col]))
799 min = i;
800 }
801 return min;
802 }
803
804 static isl_stat inv_exchange(__isl_keep isl_mat **left,
805 __isl_keep isl_mat **right, unsigned i, unsigned j)
806 {
807 *left = isl_mat_swap_rows(*left, i, j);
808 *right = isl_mat_swap_rows(*right, i, j);
809
810 if (!*left || !*right)
811 return isl_stat_error;
812 return isl_stat_ok;
813 }
814
815 static void inv_oppose(
816 struct isl_mat *left, struct isl_mat *right, unsigned row)
817 {
818 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
819 isl_seq_neg(right->row[row], right->row[row], right->n_col);
820 }
821
822 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
823 unsigned row, unsigned i, isl_int m)
824 {
825 isl_int_neg(m, m);
826 isl_seq_combine(left->row[i]+row,
827 left->ctx->one, left->row[i]+row,
828 m, left->row[row]+row,
829 left->n_col-row);
830 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
831 m, right->row[row], right->n_col);
832 }
833
834 /* Compute inv(left)*right
835 */
836 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
837 struct isl_mat *right)
838 {
839 int row;
840 isl_int a, b;
841
842 if (!left || !right)
843 goto error;
844
845 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
846 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
847
848 if (left->n_row == 0) {
849 isl_mat_free(left);
850 return right;
851 }
852
853 left = isl_mat_cow(left);
854 right = isl_mat_cow(right);
855 if (!left || !right)
856 goto error;
857
858 isl_int_init(a);
859 isl_int_init(b);
860 for (row = 0; row < left->n_row; ++row) {
861 int pivot, first, i, off;
862 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
863 if (pivot < 0) {
864 isl_int_clear(a);
865 isl_int_clear(b);
866 isl_assert(left->ctx, pivot >= 0, goto error);
867 }
868 pivot += row;
869 if (pivot != row)
870 if (inv_exchange(&left, &right, pivot, row) < 0)
871 goto error;
872 if (isl_int_is_neg(left->row[row][row]))
873 inv_oppose(left, right, row);
874 first = row+1;
875 while ((off = row_first_non_zero(left->row+first,
876 left->n_row-first, row)) != -1) {
877 first += off;
878 isl_int_fdiv_q(a, left->row[first][row],
879 left->row[row][row]);
880 inv_subtract(left, right, row, first, a);
881 if (!isl_int_is_zero(left->row[first][row])) {
882 if (inv_exchange(&left, &right, row, first) < 0)
883 goto error;
884 } else {
885 ++first;
886 }
887 }
888 for (i = 0; i < row; ++i) {
889 if (isl_int_is_zero(left->row[i][row]))
890 continue;
891 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
892 isl_int_divexact(b, left->row[i][row], a);
893 isl_int_divexact(a, left->row[row][row], a);
894 isl_int_neg(b, b);
895 isl_seq_combine(left->row[i] + i,
896 a, left->row[i] + i,
897 b, left->row[row] + i,
898 left->n_col - i);
899 isl_seq_combine(right->row[i], a, right->row[i],
900 b, right->row[row], right->n_col);
901 }
902 }
903 isl_int_clear(b);
904
905 isl_int_set(a, left->row[0][0]);
906 for (row = 1; row < left->n_row; ++row)
907 isl_int_lcm(a, a, left->row[row][row]);
908 if (isl_int_is_zero(a)){
909 isl_int_clear(a);
910 isl_assert(left->ctx, 0, goto error);
911 }
912 for (row = 0; row < left->n_row; ++row) {
913 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
914 if (isl_int_is_one(left->row[row][row]))
915 continue;
916 isl_seq_scale(right->row[row], right->row[row],
917 left->row[row][row], right->n_col);
918 }
919 isl_int_clear(a);
920
921 isl_mat_free(left);
922 return right;
923 error:
924 isl_mat_free(left);
925 isl_mat_free(right);
926 return NULL;
927 }
928
929 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
930 {
931 int i;
932
933 for (i = 0; i < mat->n_row; ++i)
934 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
935 }
936
937 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
938 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
939 {
940 int i;
941 isl_int tmp;
942
943 isl_int_init(tmp);
944 for (i = 0; i < mat->n_row; ++i) {
945 isl_int_mul(tmp, m1, mat->row[i][src1]);
946 isl_int_addmul(tmp, m2, mat->row[i][src2]);
947 isl_int_set(mat->row[i][dst], tmp);
948 }
949 isl_int_clear(tmp);
950 }
951
952 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
953 {
954 struct isl_mat *inv;
955 int row;
956 isl_int a, b;
957
958 mat = isl_mat_cow(mat);
959 if (!mat)
960 return NULL;
961
962 inv = isl_mat_identity(mat->ctx, mat->n_col);
963 inv = isl_mat_cow(inv);
964 if (!inv)
965 goto error;
966
967 isl_int_init(a);
968 isl_int_init(b);
969 for (row = 0; row < mat->n_row; ++row) {
970 int pivot, first, i, off;
971 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
972 if (pivot < 0) {
973 isl_int_clear(a);
974 isl_int_clear(b);
975 isl_assert(mat->ctx, pivot >= 0, goto error);
976 }
977 pivot += row;
978 if (pivot != row)
979 exchange(mat, &inv, NULL, row, pivot, row);
980 if (isl_int_is_neg(mat->row[row][row]))
981 oppose(mat, &inv, NULL, row, row);
982 first = row+1;
983 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
984 mat->n_col-first)) != -1) {
985 first += off;
986 isl_int_fdiv_q(a, mat->row[row][first],
987 mat->row[row][row]);
988 subtract(mat, &inv, NULL, row, row, first, a);
989 if (!isl_int_is_zero(mat->row[row][first]))
990 exchange(mat, &inv, NULL, row, row, first);
991 else
992 ++first;
993 }
994 for (i = 0; i < row; ++i) {
995 if (isl_int_is_zero(mat->row[row][i]))
996 continue;
997 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
998 isl_int_divexact(b, mat->row[row][i], a);
999 isl_int_divexact(a, mat->row[row][row], a);
1000 isl_int_neg(a, a);
1001 isl_mat_col_combine(mat, i, a, i, b, row);
1002 isl_mat_col_combine(inv, i, a, i, b, row);
1003 }
1004 }
1005 isl_int_clear(b);
1006
1007 isl_int_set(a, mat->row[0][0]);
1008 for (row = 1; row < mat->n_row; ++row)
1009 isl_int_lcm(a, a, mat->row[row][row]);
1010 if (isl_int_is_zero(a)){
1011 isl_int_clear(a);
1012 goto error;
1013 }
1014 for (row = 0; row < mat->n_row; ++row) {
1015 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
1016 if (isl_int_is_one(mat->row[row][row]))
1017 continue;
1018 isl_mat_col_scale(inv, row, mat->row[row][row]);
1019 }
1020 isl_int_clear(a);
1021
1022 isl_mat_free(mat);
1023
1024 return inv;
1025 error:
1026 isl_mat_free(mat);
1027 isl_mat_free(inv);
1028 return NULL;
1029 }
1030
1031 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
1032 {
1033 struct isl_mat *transpose = NULL;
1034 int i, j;
1035
1036 if (!mat)
1037 return NULL;
1038
1039 if (mat->n_col == mat->n_row) {
1040 mat = isl_mat_cow(mat);
1041 if (!mat)
1042 return NULL;
1043 for (i = 0; i < mat->n_row; ++i)
1044 for (j = i + 1; j < mat->n_col; ++j)
1045 isl_int_swap(mat->row[i][j], mat->row[j][i]);
1046 return mat;
1047 }
1048 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
1049 if (!transpose)
1050 goto error;
1051 for (i = 0; i < mat->n_row; ++i)
1052 for (j = 0; j < mat->n_col; ++j)
1053 isl_int_set(transpose->row[j][i], mat->row[i][j]);
1054 isl_mat_free(mat);
1055 return transpose;
1056 error:
1057 isl_mat_free(mat);
1058 return NULL;
1059 }
1060
1061 __isl_give isl_mat *isl_mat_swap_cols(__isl_take isl_mat *mat,
1062 unsigned i, unsigned j)
1063 {
1064 int r;
1065
1066 mat = isl_mat_cow(mat);
1067 if (!mat)
1068 return NULL;
1069 isl_assert(mat->ctx, i < mat->n_col, goto error);
1070 isl_assert(mat->ctx, j < mat->n_col, goto error);
1071
1072 for (r = 0; r < mat->n_row; ++r)
1073 isl_int_swap(mat->row[r][i], mat->row[r][j]);
1074 return mat;
1075 error:
1076 isl_mat_free(mat);
1077 return NULL;
1078 }
1079
1080 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
1081 {
1082 isl_int *t;
1083
1084 if (!mat)
1085 return NULL;
1086 mat = isl_mat_cow(mat);
1087 if (!mat)
1088 return NULL;
1089 t = mat->row[i];
1090 mat->row[i] = mat->row[j];
1091 mat->row[j] = t;
1092 return mat;
1093 }
1094
1095 /* Calculate the product of two matrices.
1096 *
1097 * This function is optimized for operand matrices that contain many zeros and
1098 * skips multiplications where we know one of the operands is zero.
1099 */
1100 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1101 __isl_take isl_mat *right)
1102 {
1103 int i, j, k;
1104 struct isl_mat *prod;
1105
1106 if (!left || !right)
1107 goto error;
1108 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1109 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1110 if (!prod)
1111 goto error;
1112 if (left->n_col == 0) {
1113 for (i = 0; i < prod->n_row; ++i)
1114 isl_seq_clr(prod->row[i], prod->n_col);
1115 isl_mat_free(left);
1116 isl_mat_free(right);
1117 return prod;
1118 }
1119 for (i = 0; i < prod->n_row; ++i) {
1120 for (j = 0; j < prod->n_col; ++j)
1121 isl_int_mul(prod->row[i][j],
1122 left->row[i][0], right->row[0][j]);
1123 for (k = 1; k < left->n_col; ++k) {
1124 if (isl_int_is_zero(left->row[i][k]))
1125 continue;
1126 for (j = 0; j < prod->n_col; ++j)
1127 isl_int_addmul(prod->row[i][j],
1128 left->row[i][k], right->row[k][j]);
1129 }
1130 }
1131 isl_mat_free(left);
1132 isl_mat_free(right);
1133 return prod;
1134 error:
1135 isl_mat_free(left);
1136 isl_mat_free(right);
1137 return NULL;
1138 }
1139
1140 /* Replace the variables x in the rows q by x' given by x = M x',
1141 * with M the matrix mat.
1142 *
1143 * If the number of new variables is greater than the original
1144 * number of variables, then the rows q have already been
1145 * preextended. If the new number is smaller, then the coefficients
1146 * of the divs, which are not changed, need to be shifted down.
1147 * The row q may be the equalities, the inequalities or the
1148 * div expressions. In the latter case, has_div is true and
1149 * we need to take into account the extra denominator column.
1150 */
1151 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1152 unsigned n_div, int has_div, struct isl_mat *mat)
1153 {
1154 int i;
1155 struct isl_mat *t;
1156 int e;
1157
1158 if (mat->n_col >= mat->n_row)
1159 e = 0;
1160 else
1161 e = mat->n_row - mat->n_col;
1162 if (has_div)
1163 for (i = 0; i < n; ++i)
1164 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1165 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1166 t = isl_mat_product(t, mat);
1167 if (!t)
1168 return -1;
1169 for (i = 0; i < n; ++i) {
1170 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1171 isl_seq_cpy(q[i] + has_div + t->n_col,
1172 q[i] + has_div + t->n_col + e, n_div);
1173 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1174 }
1175 isl_mat_free(t);
1176 return 0;
1177 }
1178
1179 /* Replace the variables x in bset by x' given by x = M x', with
1180 * M the matrix mat.
1181 *
1182 * If there are fewer variables x' then there are x, then we perform
1183 * the transformation in place, which means that, in principle,
1184 * this frees up some extra variables as the number
1185 * of columns remains constant, but we would have to extend
1186 * the div array too as the number of rows in this array is assumed
1187 * to be equal to extra.
1188 */
1189 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1190 struct isl_mat *mat)
1191 {
1192 struct isl_ctx *ctx;
1193
1194 if (!bset || !mat)
1195 goto error;
1196
1197 ctx = bset->ctx;
1198 bset = isl_basic_set_cow(bset);
1199 if (!bset)
1200 goto error;
1201
1202 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1203 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1204 isl_assert(ctx, mat->n_col > 0, goto error);
1205
1206 if (mat->n_col > mat->n_row) {
1207 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1208 if (!bset)
1209 goto error;
1210 } else if (mat->n_col < mat->n_row) {
1211 bset->dim = isl_space_cow(bset->dim);
1212 if (!bset->dim)
1213 goto error;
1214 bset->dim->n_out -= mat->n_row - mat->n_col;
1215 }
1216
1217 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1218 isl_mat_copy(mat)) < 0)
1219 goto error;
1220
1221 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1222 isl_mat_copy(mat)) < 0)
1223 goto error;
1224
1225 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1226 goto error2;
1227
1228 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1229 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1230 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1231 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1232 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1233
1234 bset = isl_basic_set_simplify(bset);
1235 bset = isl_basic_set_finalize(bset);
1236
1237 return bset;
1238 error:
1239 isl_mat_free(mat);
1240 error2:
1241 isl_basic_set_free(bset);
1242 return NULL;
1243 }
1244
1245 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1246 {
1247 int i;
1248
1249 set = isl_set_cow(set);
1250 if (!set)
1251 goto error;
1252
1253 for (i = 0; i < set->n; ++i) {
1254 set->p[i] = isl_basic_set_preimage(set->p[i],
1255 isl_mat_copy(mat));
1256 if (!set->p[i])
1257 goto error;
1258 }
1259 if (mat->n_col != mat->n_row) {
1260 set->dim = isl_space_cow(set->dim);
1261 if (!set->dim)
1262 goto error;
1263 set->dim->n_out += mat->n_col;
1264 set->dim->n_out -= mat->n_row;
1265 }
1266 isl_mat_free(mat);
1267 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1268 return set;
1269 error:
1270 isl_set_free(set);
1271 isl_mat_free(mat);
1272 return NULL;
1273 }
1274
1275 /* Replace the variables x starting at "first_col" in the rows "rows"
1276 * of some coefficient matrix by x' with x = M x' with M the matrix mat.
1277 * That is, replace the corresponding coefficients c by c M.
1278 */
1279 isl_stat isl_mat_sub_transform(isl_int **row, unsigned n_row,
1280 unsigned first_col, __isl_take isl_mat *mat)
1281 {
1282 int i;
1283 isl_ctx *ctx;
1284 isl_mat *t;
1285
1286 if (!mat)
1287 return isl_stat_error;
1288 ctx = isl_mat_get_ctx(mat);
1289 t = isl_mat_sub_alloc6(ctx, row, 0, n_row, first_col, mat->n_row);
1290 t = isl_mat_product(t, mat);
1291 if (!t)
1292 return isl_stat_error;
1293 for (i = 0; i < n_row; ++i)
1294 isl_seq_swp_or_cpy(row[i] + first_col, t->row[i], t->n_col);
1295 isl_mat_free(t);
1296 return isl_stat_ok;
1297 }
1298
1299 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1300 {
1301 int i, j;
1302
1303 if (!mat) {
1304 fprintf(out, "%*snull mat\n", indent, "");
1305 return;
1306 }
1307
1308 if (mat->n_row == 0)
1309 fprintf(out, "%*s[]\n", indent, "");
1310
1311 for (i = 0; i < mat->n_row; ++i) {
1312 if (!i)
1313 fprintf(out, "%*s[[", indent, "");
1314 else
1315 fprintf(out, "%*s[", indent+1, "");
1316 for (j = 0; j < mat->n_col; ++j) {
1317 if (j)
1318 fprintf(out, ",");
1319 isl_int_print(out, mat->row[i][j], 0);
1320 }
1321 if (i == mat->n_row-1)
1322 fprintf(out, "]]\n");
1323 else
1324 fprintf(out, "]\n");
1325 }
1326 }
1327
1328 void isl_mat_dump(__isl_keep isl_mat *mat)
1329 {
1330 isl_mat_print_internal(mat, stderr, 0);
1331 }
1332
1333 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1334 {
1335 int r;
1336
1337 if (n == 0)
1338 return mat;
1339
1340 mat = isl_mat_cow(mat);
1341 if (!mat)
1342 return NULL;
1343
1344 if (col != mat->n_col-n) {
1345 for (r = 0; r < mat->n_row; ++r)
1346 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1347 mat->n_col - col - n);
1348 }
1349 mat->n_col -= n;
1350 return mat;
1351 }
1352
1353 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1354 {
1355 int r;
1356
1357 mat = isl_mat_cow(mat);
1358 if (!mat)
1359 return NULL;
1360
1361 for (r = row; r+n < mat->n_row; ++r)
1362 mat->row[r] = mat->row[r+n];
1363
1364 mat->n_row -= n;
1365 return mat;
1366 }
1367
1368 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1369 unsigned col, unsigned n)
1370 {
1371 isl_mat *ext;
1372
1373 if (!mat)
1374 return NULL;
1375 if (n == 0)
1376 return mat;
1377
1378 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1379 if (!ext)
1380 goto error;
1381
1382 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1383 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1384 col + n, col, mat->n_col - col);
1385
1386 isl_mat_free(mat);
1387 return ext;
1388 error:
1389 isl_mat_free(mat);
1390 return NULL;
1391 }
1392
1393 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1394 unsigned first, unsigned n)
1395 {
1396 int i;
1397
1398 if (!mat)
1399 return NULL;
1400 mat = isl_mat_insert_cols(mat, first, n);
1401 if (!mat)
1402 return NULL;
1403
1404 for (i = 0; i < mat->n_row; ++i)
1405 isl_seq_clr(mat->row[i] + first, n);
1406
1407 return mat;
1408 }
1409
1410 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1411 {
1412 if (!mat)
1413 return NULL;
1414
1415 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1416 }
1417
1418 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1419 unsigned row, unsigned n)
1420 {
1421 isl_mat *ext;
1422
1423 if (!mat)
1424 return NULL;
1425 if (n == 0)
1426 return mat;
1427
1428 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1429 if (!ext)
1430 goto error;
1431
1432 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1433 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1434 mat->n_row - row, 0, 0, mat->n_col);
1435
1436 isl_mat_free(mat);
1437 return ext;
1438 error:
1439 isl_mat_free(mat);
1440 return NULL;
1441 }
1442
1443 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1444 {
1445 if (!mat)
1446 return NULL;
1447
1448 return isl_mat_insert_rows(mat, mat->n_row, n);
1449 }
1450
1451 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1452 unsigned row, unsigned n)
1453 {
1454 int i;
1455
1456 mat = isl_mat_insert_rows(mat, row, n);
1457 if (!mat)
1458 return NULL;
1459
1460 for (i = 0; i < n; ++i)
1461 isl_seq_clr(mat->row[row + i], mat->n_col);
1462
1463 return mat;
1464 }
1465
1466 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1467 {
1468 if (!mat)
1469 return NULL;
1470
1471 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1472 }
1473
1474 void isl_mat_col_submul(struct isl_mat *mat,
1475 int dst_col, isl_int f, int src_col)
1476 {
1477 int i;
1478
1479 for (i = 0; i < mat->n_row; ++i)
1480 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1481 }
1482
1483 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1484 {
1485 int i;
1486
1487 if (!mat)
1488 return;
1489
1490 for (i = 0; i < mat->n_row; ++i)
1491 isl_int_add(mat->row[i][dst_col],
1492 mat->row[i][dst_col], mat->row[i][src_col]);
1493 }
1494
1495 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1496 {
1497 int i;
1498
1499 for (i = 0; i < mat->n_row; ++i)
1500 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1501 }
1502
1503 /* Add "f" times column "src_col" to column "dst_col" of "mat" and
1504 * return the result.
1505 */
1506 __isl_give isl_mat *isl_mat_col_addmul(__isl_take isl_mat *mat, int dst_col,
1507 isl_int f, int src_col)
1508 {
1509 int i;
1510
1511 if (check_col(mat, dst_col) < 0 || check_col(mat, src_col) < 0)
1512 return isl_mat_free(mat);
1513
1514 for (i = 0; i < mat->n_row; ++i) {
1515 if (isl_int_is_zero(mat->row[i][src_col]))
1516 continue;
1517 mat = isl_mat_cow(mat);
1518 if (!mat)
1519 return NULL;
1520 isl_int_addmul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1521 }
1522
1523 return mat;
1524 }
1525
1526 /* Negate column "col" of "mat" and return the result.
1527 */
1528 __isl_give isl_mat *isl_mat_col_neg(__isl_take isl_mat *mat, int col)
1529 {
1530 int i;
1531
1532 if (check_col(mat, col) < 0)
1533 return isl_mat_free(mat);
1534
1535 for (i = 0; i < mat->n_row; ++i) {
1536 if (isl_int_is_zero(mat->row[i][col]))
1537 continue;
1538 mat = isl_mat_cow(mat);
1539 if (!mat)
1540 return NULL;
1541 isl_int_neg(mat->row[i][col], mat->row[i][col]);
1542 }
1543
1544 return mat;
1545 }
1546
1547 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1548 {
1549 int r;
1550 struct isl_mat *H = NULL, *Q = NULL;
1551
1552 if (!M)
1553 return NULL;
1554
1555 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1556 M->n_row = row;
1557 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1558 M->n_row = M->n_col;
1559 if (!H)
1560 goto error;
1561 for (r = 0; r < row; ++r)
1562 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1563 for (r = row; r < M->n_row; ++r)
1564 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1565 isl_mat_free(H);
1566 isl_mat_free(Q);
1567 return M;
1568 error:
1569 isl_mat_free(H);
1570 isl_mat_free(Q);
1571 isl_mat_free(M);
1572 return NULL;
1573 }
1574
1575 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1576 __isl_take isl_mat *bot)
1577 {
1578 struct isl_mat *mat;
1579
1580 if (!top || !bot)
1581 goto error;
1582
1583 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1584 if (top->n_row == 0) {
1585 isl_mat_free(top);
1586 return bot;
1587 }
1588 if (bot->n_row == 0) {
1589 isl_mat_free(bot);
1590 return top;
1591 }
1592
1593 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1594 if (!mat)
1595 goto error;
1596 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1597 0, 0, mat->n_col);
1598 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1599 0, 0, mat->n_col);
1600 isl_mat_free(top);
1601 isl_mat_free(bot);
1602 return mat;
1603 error:
1604 isl_mat_free(top);
1605 isl_mat_free(bot);
1606 return NULL;
1607 }
1608
1609 isl_bool isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1610 {
1611 int i;
1612
1613 if (!mat1 || !mat2)
1614 return isl_bool_error;
1615
1616 if (mat1->n_row != mat2->n_row)
1617 return isl_bool_false;
1618
1619 if (mat1->n_col != mat2->n_col)
1620 return isl_bool_false;
1621
1622 for (i = 0; i < mat1->n_row; ++i)
1623 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1624 return isl_bool_false;
1625
1626 return isl_bool_true;
1627 }
1628
1629 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1630 {
1631 struct isl_mat *mat;
1632
1633 if (!vec)
1634 return NULL;
1635 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1636 if (!mat)
1637 goto error;
1638
1639 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1640
1641 isl_vec_free(vec);
1642 return mat;
1643 error:
1644 isl_vec_free(vec);
1645 return NULL;
1646 }
1647
1648 /* Return a copy of row "row" of "mat" as an isl_vec.
1649 */
1650 __isl_give isl_vec *isl_mat_get_row(__isl_keep isl_mat *mat, unsigned row)
1651 {
1652 isl_vec *v;
1653
1654 if (!mat)
1655 return NULL;
1656 if (row >= mat->n_row)
1657 isl_die(mat->ctx, isl_error_invalid, "row out of range",
1658 return NULL);
1659
1660 v = isl_vec_alloc(isl_mat_get_ctx(mat), mat->n_col);
1661 if (!v)
1662 return NULL;
1663 isl_seq_cpy(v->el, mat->row[row], mat->n_col);
1664
1665 return v;
1666 }
1667
1668 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1669 __isl_take isl_vec *bot)
1670 {
1671 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1672 }
1673
1674 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1675 unsigned dst_col, unsigned src_col, unsigned n)
1676 {
1677 isl_mat *res;
1678
1679 if (!mat)
1680 return NULL;
1681 if (n == 0 || dst_col == src_col)
1682 return mat;
1683
1684 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1685 if (!res)
1686 goto error;
1687
1688 if (dst_col < src_col) {
1689 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1690 0, 0, dst_col);
1691 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1692 dst_col, src_col, n);
1693 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1694 dst_col + n, dst_col, src_col - dst_col);
1695 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1696 src_col + n, src_col + n,
1697 res->n_col - src_col - n);
1698 } else {
1699 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1700 0, 0, src_col);
1701 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1702 src_col, src_col + n, dst_col - src_col);
1703 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1704 dst_col, src_col, n);
1705 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1706 dst_col + n, dst_col + n,
1707 res->n_col - dst_col - n);
1708 }
1709 isl_mat_free(mat);
1710
1711 return res;
1712 error:
1713 isl_mat_free(mat);
1714 return NULL;
1715 }
1716
1717 /* Return the gcd of the elements in row "row" of "mat" in *gcd.
1718 * Return isl_stat_ok on success and isl_stat_error on failure.
1719 */
1720 isl_stat isl_mat_row_gcd(__isl_keep isl_mat *mat, int row, isl_int *gcd)
1721 {
1722 if (!mat)
1723 return isl_stat_error;
1724
1725 if (row < 0 || row >= mat->n_row)
1726 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
1727 "row out of range", return isl_stat_error);
1728 isl_seq_gcd(mat->row[row], mat->n_col, gcd);
1729
1730 return isl_stat_ok;
1731 }
1732
1733 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1734 {
1735 int i;
1736 isl_int g;
1737
1738 isl_int_set_si(*gcd, 0);
1739 if (!mat)
1740 return;
1741
1742 isl_int_init(g);
1743 for (i = 0; i < mat->n_row; ++i) {
1744 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1745 isl_int_gcd(*gcd, *gcd, g);
1746 }
1747 isl_int_clear(g);
1748 }
1749
1750 /* Return the result of scaling "mat" by a factor of "m".
1751 */
1752 __isl_give isl_mat *isl_mat_scale(__isl_take isl_mat *mat, isl_int m)
1753 {
1754 int i;
1755
1756 if (isl_int_is_one(m))
1757 return mat;
1758
1759 mat = isl_mat_cow(mat);
1760 if (!mat)
1761 return NULL;
1762
1763 for (i = 0; i < mat->n_row; ++i)
1764 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
1765
1766 return mat;
1767 }
1768
1769 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1770 {
1771 int i;
1772
1773 if (isl_int_is_one(m))
1774 return mat;
1775
1776 mat = isl_mat_cow(mat);
1777 if (!mat)
1778 return NULL;
1779
1780 for (i = 0; i < mat->n_row; ++i)
1781 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1782
1783 return mat;
1784 }
1785
1786 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1787 isl_int m)
1788 {
1789 if (isl_int_is_one(m))
1790 return mat;
1791
1792 mat = isl_mat_cow(mat);
1793 if (!mat)
1794 return NULL;
1795
1796 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1797
1798 return mat;
1799 }
1800
1801 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1802 {
1803 isl_int gcd;
1804
1805 if (!mat)
1806 return NULL;
1807
1808 isl_int_init(gcd);
1809 isl_mat_gcd(mat, &gcd);
1810 mat = isl_mat_scale_down(mat, gcd);
1811 isl_int_clear(gcd);
1812
1813 return mat;
1814 }
1815
1816 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1817 {
1818 mat = isl_mat_cow(mat);
1819 if (!mat)
1820 return NULL;
1821
1822 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1823
1824 return mat;
1825 }
1826
1827 /* Number of initial non-zero columns.
1828 */
1829 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1830 {
1831 int i;
1832
1833 if (!mat)
1834 return -1;
1835
1836 for (i = 0; i < mat->n_col; ++i)
1837 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1838 break;
1839
1840 return i;
1841 }
Integer set library